on ice harnesses:

spotting the skater as he/she learns new jumps
http://www.youtube.com/watch?v=dgCsIwQFzdA
http://www.youtube.com/watch?v=iKL9f2tGZGA
http://www.youtube.com/watch?v=nNR4ibDs-8Q
http://www.youtube.com/watch?v=wqJaHdZnryA&feature=related
http://www.youtube.com/watch?v=pBr_zIhA6m8&feature=related





Off ice harness:

used to help skaters increase rotation speed, vesibular training so they don't get dizzy, and correct posture in the air so they don't go off kilter mid way through a jump
This is two ways to use it.
http://www.youtube.com/watch?v=hw0BNkLWQPA
http://www.youtube.com/watch?v=fltgxgEl1GI

the other way the off ice one is used is to just jump like on ice, practicing the rotation and landing.